Question

volume of right circular cylinder with the height equal to the radius is 25 1/7 cm 3. find the height of the cylinder?


please answer me​

Answer 1

Answer:

The height of the cylinder is 2 cm.

Step-by-step-explanation:

We have given that,

Volume of cylinder $\displaystyle{\sf\:=\:25\:\dfrac{1}{7}\:cm^3}$

Height of cylinder ( h ) = Radius of cylinder ( r )

We have to find the height of the cylinder.

Now, we know that,

$\displaystyle{\boxed{\pink{\sf\:Volume\:of\:cylinder\:=\:\pi\:r^2\:h\:}}}$

$\displaystyle{\implies\sf\:25\:\dfrac{1}{7}\:=\:\dfrac{22}{7}\:\times\:h^2\:\times\:h\:\qquad\cdots[\:\because\:r\:=\:h\:]}$

$\displaystyle{\implies\sf\:\dfrac{25\:\times\:7\:+\:1}{7}\:=\:\dfrac{22}{7}\:\times\:h^3}$

$\displaystyle{\implies\sf\:h^3\:=\:\dfrac{175\:+\:1}{\cancel{7}}\:\times\:\dfrac{\cancel{7}}{22}}$

$\displaystyle{\implies\sf\:h^3\:=\:\cancel{\dfrac{176}{22}}}$

$\displaystyle{\implies\sf\:h^3\:=\:8}$

$\displaystyle{\implies\sf\:\sqrt[3]{\sf{h^3}}\:=\:\sqrt[3]{\sf{8}}}$

$\displaystyle{\implies\sf\:h\:=\:2}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:Height\:=\:2\:cm\:}}}}$

∴ The height of the cylinder is 2 cm.

Answer 2

★GIVEN:-

volume of right circular cylinder with the height equal to the radius is 25 1/7 cm ^3.

★FIND:-

• height of cylinder

★SOLUTION:-

• we know that cylinder volume formula

$\implies \red{ \pi \: r {}^{2} h}$

• and given that cylinder volume 25 1/7 cm^3

and height =radius

we find height so let radius =h

question according

$\implies \: \pi \: h {}^{2}h = 25 \: \frac{1}{7} \\ \\ \implies \: h {}^{3} = \frac{ \cancel{7}(25 \times 7 + 1)}{ \cancel7 \times 22} \\ \\ \implies \: h {}^{3} = \cancel{\frac{176}{22}}$

• h^3=8

• h^3=2^3

• h=2

therefore cylinder height=2 cm

and radius =2×2=4 cm

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I hope it helps you